st: Survey analysis: Why does PSU affect proportions?

I am using a published dataset (from CDC) and I want to verify that I
can duplicate the published results before I begin my analysis. I
found that including clustering and stratification variables changed
proportions, not only standard errors. In the output that follows, I
first used only the weights. This gives results that agree with the
published estimates of the proportions (produced using SUDAAN). Next
I used the PSU and STRATA, and get different proportions, but
confidence intervals that agree with the published results, with
minor variations in other runs. I don't think the clustering by
strata and psu should influence proportions, only their variance.

The dataset documentation says that a three-state cluster sample was
used, but only the WEIGHT, PSU, and STRATA are included in the public
dataset. The FAQ (Survey-data analysis, first item) says that this
sort of svyset statement will produce appropriate variance estimates
for multistate designs. Am I doing something wrong?